I have a question that isn't immediately relevant to me, and I'm not sure will be important in the future as I am quite happy with my situation. It is however something I have thought about at length and I've yet to come up with a set of general guidelines. I am a graduate student in the United States studying Mathematics, and am currently working with an advisor who has graduated ~10 students in his career. He has in the past mentioned a couple of the students, both in the context of research and current careers.
Is it appropriate to ask my advisor's former students questions regarding my relationship with said advisor? If this is a normal practice (as the question below would suggest), what is the etiquette to use in this situation? In particular, I am asking in the case where the previous students have all moved on and already graduated so email seems to be the best method of reaching out. Also, given that these conversations could contain sensitive information (i.e. questions regarding funding options given to the student, or grievances with said advisor) what would be the "kind" way to prevent the "sensitive" parts of the conversation from being relayed back to the advisor? Finally, would it be wise to reach out to some of these former student's at some point in my studies just for introduction and networking purposes? It is unlikely that our research interests would line up exactly, but it is an opportunity to contact people who have been through the same experience.
A specific case that is could become relevant in the future:
One of my advisor's recent students went into industry, and if this was something I considered in the future, would it be intrusive to email them and ask about their transition from graduate school to industry? In particular, would asking questions specific to my advisor's thoughts on this transition be appropriate? Also, related to the sensitive part, if for whatever reason I didn't want the advisor to know this was something I was considering would it be okay to ask the former student to keep this between us?
Note, I thought there would be many threads with a similar question, but the closest thing searches brought up was this link.